A uniform wire of length l and weight w is suspended from the roof with a weight W at the other end. The stress in the wire at a distance l/3 from the top is (W/A+2/γw/A), where A is the cross-sectional area of the wire. The value of γ is .

Question

Accepted Answer

3. Idea: a cross-section of the wire carries everything hanging below it — the load W plus the weight of the wire below that section. At l/3 from the top, the length below is l-l/3=(2l)/3, which weighs 2/3w since the wire is uniform. Tension there is T=W+2/3w, so the stress is W/A+2/3w/A. Comparing with W/A+2/γw/A gives 2/γ=2/3. Hence γ=3.

A uniform wire of length l and weight w is suspended from the roof with a weight W at the other end. The stress in the wire at a distance l/3 from the top is (W/A+2/γw/A), where A is the cross-sectional area of the wire. The value of γ is ______.

Step-by-step solution